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Add footnote on Frege contributed by R. Heck; fixes issue #342
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Richard Heck authored and rzach committed Dec 15, 2023
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10 changes: 8 additions & 2 deletions bib/open-logic.bib
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Expand Up @@ -296,6 +296,14 @@ @article{Grattan-Guinness1971
year = 1971,
}

@book{Heck2012,
author = {Richard Kimberly Heck},
title = {Reading Frege's Grundgesetze},
publisher = {Oxford University Press},
year = {2012},
address = {Oxford}
}

@book{Hodges2014,
title = {Alan Turing: The Enigma},
author = {Hodges, Andrew},
Expand All @@ -304,8 +312,6 @@ @book{Hodges2014
address = {London}
}



@misc{Imitation2014,
author = {Morten Tyldum},
title = {The Imitation Game},
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15 changes: 9 additions & 6 deletions content/set-theory/story/grundgesetze.tex
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Expand Up @@ -15,12 +15,15 @@
Paradox.

Frege's system is \emph{second-order}, and was designed to formulate
the notion of an \emph{extension of a concept}. Using notation
inspired by Frege, we will write $\fregeext{x}{F(x)}$ for \emph{the extension
of the concept $F$}. This is a device which takes a \emph{predicate},
``$F$'', and turns it into a (first-order) \emph{term},
``$\fregeext{x}{F(x)}$''. Using this device, Frege offered the following
\emph{definition} of membership:
the notion of an \emph{extension of a concept}.\footnote{Strictly
speaking, Frege attempts to formalize a more general notion: the
``value-range'' of a function. Extensions of concepts are a special
case of the more general notion. See \citet[pp.\ 8--9]{Heck2012} for
the details.} Using notation inspired by Frege, we will write
$\fregeext{x}{F(x)}$ for \emph{the extension of the concept~$F$}. This
is a device which takes a \emph{predicate}, ``$F$'', and turns it into
a (first-order) \emph{term}, ``$\fregeext{x}{F(x)}$''. Using this
device, Frege offered the following \emph{definition} of membership:
\[
a \in b =_\text{df} \exists G(b = \fregeext{x}{G(x)} \land Ga)
\]
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